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Metaphysics and Logic Seminar: Greg Restall (58吃瓜)

3rd July 2024 @ 3:00 pm - 5:00 pm
Title:听What do we听mean? Semantics, Practices and Pluralism
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Abstract:听In this informal talk, I will revisit some longstanding issues in philosophical logic in the light of some contemporary developments.听
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The longstanding issues? (1) Michael Dummett鈥檚 challenge in听The Logical Basis of Metaphysics听to the effect that to get anywhere in fundamental issues of metaphysics we would do well to attend to the fundamental commitments of our theory of meaning鈥攁nd that those concerns lead to the conclusion that we can find common ground in intuitionistic logic, not classical logic. (2) The issue of听pluralism听(or听monism) about logical consequence. Contemporary work in logic is filled with a range of different (and seemingly opposed) accounts of what follows from what. Many different kinds of logical听pluralism听have arisen to attempt to make sense of the diversity of logical analyses, and just as many defences of logical听monism听have been offered.
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The contemporary developments? The rise of听dependent type theory听in computer science and the consequent rise of听proof assistants听in the formalisation of mathematics. Different proof assistants (Agda, Idris, Lean, Isabelle, Coq) make different choices in the formal representation of mathematical reasoning, but the predominant听choice of these proof assistants is to represent proofs听constructively, in what amounts to听intuitionistic logic听and not classical logic. Proof assistants are steadily gaining ground in the mathematical community鈥攎athematicians use these tools as conversation partners in the development of mathematical proofs, and many of these conversation partners have intuitionistic scruples.听
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I will reexamine Dummett鈥檚 appeal to revisit fundamental commitments in our theory of meaning, and the challenge of logical pluralism, given the example of the use of proof assistants in mathematical reasoning. We will see that paying attention to different aspects of our reasoning practices can clarify what is at stake in debates over the use of this or that logic, or about the propriety of some semantic principle. In the end, I hope to show that鈥攁s Dummett argued鈥攊t is worthwhile to spend听some听time attending to the concepts we use in our theorising, just as the astronomer must take care of her telescopes if she wants to see clearly and see far, and understand the power and limits of her tools. However, I will also show that taking Dummett鈥檚 advice does听not听mean that we must accept his restrictive conclusion about the impropriety of classical reasoning. Classical reasoning can be vindicated, but at some cost.

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